Journal of Graph Theory, ISSN 0364-9024, 09/2017, Volume 86, Issue 1, pp. 78 - 91

A noncomplete graph Γ is said to be (G, 2)‐distance transitive if G is a subgroup of the automorphism group of Γ that is transitive on the vertex set of Γ, and...

20B25 | 2010 Mathematics Subject Classification. 05E18 | permutation group | 05E18 | 20B25. 2‐distance transitive graph | 2‐arc transitive graph | 2-arc transitive graph | 20B25. 2-distance transitive graph | MATHEMATICS | 2-distance transitive graph | 2010 Mathematics Subject Classification

20B25 | 2010 Mathematics Subject Classification. 05E18 | permutation group | 05E18 | 20B25. 2‐distance transitive graph | 2‐arc transitive graph | 2-arc transitive graph | 20B25. 2-distance transitive graph | MATHEMATICS | 2-distance transitive graph | 2010 Mathematics Subject Classification

Journal Article

Combinatorica, ISSN 0209-9683, 8/2019, Volume 39, Issue 4, pp. 933 - 960

This paper initiates a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic...

60G57 | 60C05 | Mathematics, general | Mathematics | 05E18 | Combinatorics

60G57 | 60C05 | Mathematics, general | Mathematics | 05E18 | Combinatorics

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2018, Volume 38, Issue 3, pp. 853 - 865

The distinguishing number (index) ) ( ′( )) of a graph is the least integer such that has a vertex labeling (edge labeling) with labels that is preserved only...

distinguishing index | 05E18 | distinguishing number | lexicographic | 05C15 | Distinguishing number | Distinguishing index | Lexicographic | MATHEMATICS

distinguishing index | 05E18 | distinguishing number | lexicographic | 05C15 | Distinguishing number | Distinguishing index | Lexicographic | MATHEMATICS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2020, Volume 40, Issue 3, pp. 875 - 884

The distinguishing number (index) ) ( ( )) of a graph is the least integer such that has an vertex (edge) labeling with labels that is preserved only by the...

distinguishing index | unicyclic graph | automorphism group | tree | 05E18 | distinguishing number | 05C15 | 05e18 | 05c15

distinguishing index | unicyclic graph | automorphism group | tree | 05E18 | distinguishing number | 05C15 | 05e18 | 05c15

Journal Article

Combinatorica (Budapest. 1981), ISSN 1439-6912, 2015, Volume 36, Issue 4, pp. 371 - 393

Let A be an abelian group and let ι be the automorphism of A defined by: ι: a ↦ a−1. A Cayley graph Γ = Cay(A,S) is said to have an automorphism group as small...

20B25 | Mathematics, general | Mathematics | 05E18 | Combinatorics | MATHEMATICS | PERMUTATION-GROUPS | SCHUR RINGS | CYCLIC GROUPS | REGULAR REPRESENTATIONS

20B25 | Mathematics, general | Mathematics | 05E18 | Combinatorics | MATHEMATICS | PERMUTATION-GROUPS | SCHUR RINGS | CYCLIC GROUPS | REGULAR REPRESENTATIONS

Journal Article

Annals of Combinatorics, ISSN 0218-0006, 6/2019, Volume 23, Issue 2, pp. 285 - 293

We classify the unimodular equivalence classes of inclusion-minimal polygons with a certain fixed lattice width. As a corollary, we find a sharp upper bound on...

Polytopes | Convex lattice polygons | Secondary 05E18 | Convex lattice | Primary 52B20 | 52C05 | Mathematics | Combinatorics | Lattice width | MATHEMATICS, APPLIED

Polytopes | Convex lattice polygons | Secondary 05E18 | Convex lattice | Primary 52B20 | 52C05 | Mathematics | Combinatorics | Lattice width | MATHEMATICS, APPLIED

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 3/2018, Volume 59, Issue 2, pp. 331 - 362

We consider the orientation-preserving actions of finite groups G on pairs $$(S^3, \Gamma )$$ (S3,Γ) , where $$\Gamma $$ Γ is a connected graph of genus...

57M60 | Computational Mathematics and Numerical Analysis | Mathematics | Extendable action | 57M15 | 05E18 | Symmetry of 3-sphere | Combinatorics | Symmetry of graph | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | SURFACES | Graphs

57M60 | Computational Mathematics and Numerical Analysis | Mathematics | Extendable action | 57M15 | 05E18 | Symmetry of 3-sphere | Combinatorics | Symmetry of graph | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | SURFACES | Graphs

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 3/2018, Volume 59, Issue 2, pp. 451 - 460

For any given finite group, Schulte and Williams (Discrete Comput Geom 54(2):444–458, 2015) establish the existence of a convex polytope whose combinatorial...

Automorphism | Group | Computational Mathematics and Numerical Analysis | Graph | Convex polytope | Mathematics | 05E18 | 52B15 | Combinatorics | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | GRAPHS | Automorphisms | Combinatorial analysis

Automorphism | Group | Computational Mathematics and Numerical Analysis | Graph | Convex polytope | Mathematics | 05E18 | 52B15 | Combinatorics | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | GRAPHS | Automorphisms | Combinatorial analysis

Journal Article

Experimental Mathematics, ISSN 1058-6458, 01/2017, Volume 26, Issue 1, pp. 54 - 61

We study surface subgroups of groups acting simply transitively on vertex sets of certain hyperbolic triangular buildings. The study is motivated by Gromov's...

periodic apartment | surface subgroup | hyperbolic building | Primary: 05E18 | Secondary: 20F67 | MATHEMATICS | SURFACE SUBGROUPS | 51E24

periodic apartment | surface subgroup | hyperbolic building | Primary: 05E18 | Secondary: 20F67 | MATHEMATICS | SURFACE SUBGROUPS | 51E24

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 08/2019, Volume 100, Issue 1, pp. 131 - 147

A classical result of Honsberger states that the number of incongruent triangles with integer sides and perimeter $n$ is the nearest integer to $n^{2}/48$ (...

2010 Mathematics subject classification | primary 52B05 | secondary 05A17 | 05E18 | 05A10 | orbit enumeration | MATHEMATICS | dihedral groups | integer polygons | perimeter | TRIANGLES | enumeration

2010 Mathematics subject classification | primary 52B05 | secondary 05A17 | 05E18 | 05A10 | orbit enumeration | MATHEMATICS | dihedral groups | integer polygons | perimeter | TRIANGLES | enumeration

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 04/2017, Volume 49, Issue 2, pp. 320 - 330

In his doctoral thesis, Snover proved that any binary (m,256,δ) code is equivalent to the Nordstrom–Robinson code or the punctured Nordstrom–Robinson code for...

20B25 | 05C25 (secondary) | 05E18 (primary) | 94B05 | MATHEMATICS | REGULAR CODES | GOETHALS | BINARY | TRANSITIVE CODES | Z-LINEAR CODES | PREPARATA | KERDOCK | SYMPLECTIC SEMIFIELD PLANES

20B25 | 05C25 (secondary) | 05E18 (primary) | 94B05 | MATHEMATICS | REGULAR CODES | GOETHALS | BINARY | TRANSITIVE CODES | Z-LINEAR CODES | PREPARATA | KERDOCK | SYMPLECTIC SEMIFIELD PLANES

Journal Article

12.
Full Text
Asymptotic and constructive methods for covering perfect hash families and covering arrays

Designs, Codes and Cryptography, ISSN 0925-1022, 4/2018, Volume 86, Issue 4, pp. 907 - 937

Covering perfect hash families represent certain covering arrays compactly. Applying two probabilistic methods to covering perfect hash families improves upon...

Information and Communication, Circuits | Conditional expectation algorithm | Asymptotic bound | 05B40 | 51E20 | Data Encryption | 05D40 | Mathematics | Covering array | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Coding and Information Theory | 05E18 | Covering perfect hash family | Combinatorics | 05B15 | PERMUTATION VECTORS | MATHEMATICS, APPLIED | SEQUENCES | HIGHER STRENGTH | ALGORITHM | SETS | STATE | COMPUTER SCIENCE, THEORY & METHODS | Family | Methods | Algorithms

Information and Communication, Circuits | Conditional expectation algorithm | Asymptotic bound | 05B40 | 51E20 | Data Encryption | 05D40 | Mathematics | Covering array | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Coding and Information Theory | 05E18 | Covering perfect hash family | Combinatorics | 05B15 | PERMUTATION VECTORS | MATHEMATICS, APPLIED | SEQUENCES | HIGHER STRENGTH | ALGORITHM | SETS | STATE | COMPUTER SCIENCE, THEORY & METHODS | Family | Methods | Algorithms

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 8/2019, Volume 87, Issue 8, pp. 1815 - 1838

The affine linear group of degree one, $$\text {AGL}(1,\mathbb {F}_q)$$ AGL ( 1 , F q ) , over the finite field $$\mathbb {F}_q$$ F q , acts sharply...

Information and Communication, Circuits | Cryptology | Constant weight code | Data Structures and Information Theory | 94B25 | Discrete Mathematics in Computer Science | Affine linear group | BIBD | Computer Science | Coding and Information Theory | Johnson bound | 05E18 | 05B05 | MATHEMATICS, APPLIED | UPPER-BOUNDS | 3-DESIGNS | COMPUTER SCIENCE, THEORY & METHODS

Information and Communication, Circuits | Cryptology | Constant weight code | Data Structures and Information Theory | 94B25 | Discrete Mathematics in Computer Science | Affine linear group | BIBD | Computer Science | Coding and Information Theory | Johnson bound | 05E18 | 05B05 | MATHEMATICS, APPLIED | UPPER-BOUNDS | 3-DESIGNS | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 5/2018, Volume 86, Issue 5, pp. 1095 - 1111

Let M(n, d) be the maximum size of a permutation array on n symbols with pairwise Hamming distance at least d. We use various combinatorial, algebraic, and...

Information and Communication, Circuits | Data Encryption | Mathematics | Permutation arrays | Finite fields | 94B25 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Permutation codes | Groups | Coding and Information Theory | 05E18 | Combinatorics | 05A05 | MATHEMATICS, APPLIED | CODES | POWERLINE COMMUNICATION | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Cytokinins | Algorithms

Information and Communication, Circuits | Data Encryption | Mathematics | Permutation arrays | Finite fields | 94B25 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Permutation codes | Groups | Coding and Information Theory | 05E18 | Combinatorics | 05A05 | MATHEMATICS, APPLIED | CODES | POWERLINE COMMUNICATION | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Cytokinins | Algorithms

Journal Article

Natural computing, ISSN 1572-9796, 2017, Volume 18, Issue 3, pp. 445 - 458

For a finite group G and a finite set A, we study various algebraic aspects of cellular automata over the configuration space $$A^G$$ A G . In this situation,...

Processor Architectures | Finite monoids | MSC 20M20 | MSC 68Q80 | Artificial Intelligence | Complex Systems | Theory of Computation | Cellular automata | Invertible cellular automata | Generating sets | MSC 05E18 | Finite groups | Computer Science | Evolutionary Biology | SEMIGROUPS | RANKS | COMPUTER SCIENCE, THEORY & METHODS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Rankings | Robots | Electric generators | Lower bounds | Algebra | Simulation | Configurations | Monoids | Number theory | Subgroups

Processor Architectures | Finite monoids | MSC 20M20 | MSC 68Q80 | Artificial Intelligence | Complex Systems | Theory of Computation | Cellular automata | Invertible cellular automata | Generating sets | MSC 05E18 | Finite groups | Computer Science | Evolutionary Biology | SEMIGROUPS | RANKS | COMPUTER SCIENCE, THEORY & METHODS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Rankings | Robots | Electric generators | Lower bounds | Algebra | Simulation | Configurations | Monoids | Number theory | Subgroups

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 9/2018, Volume 48, Issue 2, pp. 179 - 225

We establish, for the character table of the symmetric group, the positivity of the row sums indexed by irreducible characters, when restricted to various...

Character tables | Symmetric power | Mathematics | 20C30 | Convex and Discrete Geometry | Exterior power | Conjugacy action | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Plethysm | 05E18 | Combinatorics | Computer Science, general | Ramanujan sum | 20C05 | 20C15 | 06A07

Character tables | Symmetric power | Mathematics | 20C30 | Convex and Discrete Geometry | Exterior power | Conjugacy action | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Plethysm | 05E18 | Combinatorics | Computer Science, general | Ramanujan sum | 20C05 | 20C15 | 06A07

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 8/2018, Volume 48, Issue 1, pp. 157 - 178

In recent work we constructed two new near octagons, one related to the finite simple group $$\mathrm {G}_2(4)$$ G2(4) and another one as a sub-near-octagon of...

Distance-regular graph | 51E12 | Mathematics | Finite simple group | 51E25 | Generalized polygon | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Commuting involutions | 05E18 | Combinatorics | Computer Science, general | Near polygon

Distance-regular graph | 51E12 | Mathematics | Finite simple group | 51E25 | Generalized polygon | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Commuting involutions | 05E18 | Combinatorics | Computer Science, general | Near polygon

Journal Article

Annals of Combinatorics, ISSN 0218-0006, 3/2016, Volume 20, Issue 1, pp. 21 - 58

The “classical” parking functions, counted by the Cayley number (n+1) n−1, carry a natural permutation representation of the symmetric group S n in which the...

diagonal harmonics | 05E10 | q, t -Catalan numbers | rational Catalan numbers | Shuffle Conjecture | 05E05 | rational parking functions | Mathematics | 05E18 | Combinatorics | q, t-Catalan numbers | MATHEMATICS, APPLIED | COMPACTIFIED JACOBIANS | STATISTICS | CONJECTURES | COMBINATORIAL FORMULA | CONTINUOUS FAMILY | CHARACTER

diagonal harmonics | 05E10 | q, t -Catalan numbers | rational Catalan numbers | Shuffle Conjecture | 05E05 | rational parking functions | Mathematics | 05E18 | Combinatorics | q, t-Catalan numbers | MATHEMATICS, APPLIED | COMPACTIFIED JACOBIANS | STATISTICS | CONJECTURES | COMBINATORIAL FORMULA | CONTINUOUS FAMILY | CHARACTER

Journal Article

Journal of algebraic combinatorics, ISSN 1572-9192, 2018, Volume 50, Issue 2, pp. 143 - 163

An m -Cayley graph $$\Gamma $$ Γ over a group G is defined as a graph which admits G as a semi-regular group of automorphisms with m orbits. This generalises...

m -Cayley graph | Symmetric graph | Mathematics | 20B25 | Double-coset graph | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | 05E18 | Combinatorics | Computer Science, general | 05C25 | Simple group | m-Cayley graph | DIHEDRAL GROUPS | MATHEMATICS | AUTOMORPHISMS | TRANSITIVE GRAPHS

m -Cayley graph | Symmetric graph | Mathematics | 20B25 | Double-coset graph | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | 05E18 | Combinatorics | Computer Science, general | 05C25 | Simple group | m-Cayley graph | DIHEDRAL GROUPS | MATHEMATICS | AUTOMORPHISMS | TRANSITIVE GRAPHS

Journal Article

20.
Full Text
Increasing Tableaux, Narayana Numbers and an Instance of the Cyclic Sieving Phenomenon

Annals of Combinatorics, ISSN 0218-0006, 9/2016, Volume 20, Issue 3, pp. 609 - 621

We give a counting formula for the set of rectangular increasing tableaux in terms of generalized Narayana numbers. We define small m–Schröder paths and give a...

cyclic sieving phenomenon | Narayana numbers | Schröder paths | Mathematics | 05E18 | Combinatorics | 05E99 | increasing tableaux | jeu de taquin | Schroder paths | MATHEMATICS, APPLIED | PROMOTION | SCHRODER NUMBERS | JEU

cyclic sieving phenomenon | Narayana numbers | Schröder paths | Mathematics | 05E18 | Combinatorics | 05E99 | increasing tableaux | jeu de taquin | Schroder paths | MATHEMATICS, APPLIED | PROMOTION | SCHRODER NUMBERS | JEU

Journal Article

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